53 is formed by the concatenation of the smallest twin primes in reverse order. [Gupta]

The sums of five, seven, and eleven consecutive Lucas numbers starting from the 53rd Lucas number, 119218851371, are primes. I.e., L(53)+...+L(57), L(53)+...+L(59), and L(53)+...+L(63) are all prime. This is the smallest Lucas number with such property. [Opao]

The prime 53 figured in the 1945 WWII battle for Iwo Jima. Task Force 53 brought the 71000 soldiers and 41000 marines. The officer commanding the Japanese troops was Lt. Gen. Tadamichi Kuribayashi, age 53. The average height of a Japanese infantryman was 5'3". Source: History TV Channel. [Haga]

1000^53 - 53 is prime. Note that 53 is the smallest number
with this property. [Firoozbakht]

The difference between the sum of unitary divisors and the value of the Euler-phi function is iterated, and started at n and a(n) is the length of terminal cycle of iteration involving a high-frequency of the prime number 53. [Labos]

The smallest two-digit prime that does not produce a prime by adding a digit to it. (There is no prime '53d'). [Gallardo]

The number of member States sitting on The United Nations Commission on Human Rights. [McAlee]

53 = prime( prime(5) + prime(3) ). Note that 53 is the only
number with this property. [Firoozbakht]